Opdracht 9b
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t-procedures for a single sample

In 1798 the English scholar Henry Cavendish measured the density of
the earth with a torsion balance.  The observed variable was the
density of the earth as a multiple of the density of water.
Cavendish's measurements are below (source: S. M. Stigler, 'Do robust
estimators work with real data?', Annals of Statistics, 5 (1977),
pp. 1055-1078.)

5.50   5.61   4.88   5.07   5.26   5.55   5.36   5.29   5.58 
5.65   5.57   5.53   5.62   5.29   5.44   5.34   5.79   5.10
5.27   5.39   5.42   5.47   5.63   5.34   5.46   5.30   5.75
5.68   5.85

The sample mean x_mean=5.45 and the sample standard deviation is s=0.22.

The data are in z:\public\share\heeringa\dicht.txt.  Read this ASCII-
file in. Define the column and choose a good variable name.

a. Draw a histogram for these measurements and combine it with 
   a normal curve.

b. Determine the 99% confidence interval.

c. Suppose that current measurements showed that the true density of
   the earth is 6.1  Are Cavendish's results then significantly 
   different from the value determined currently?  Formulate the
   appropriate H_0 and H_a.